Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control

Abstract

Text-book concepts of diffusion- versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants -- the inverse of the mean-first-passage-time to the reaction-event. In contradistinction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly-solvable model we study the conspiratory effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delimited by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.

References in corpus (12)

• Diffusion with Stochastic Resetting
• Geometry-controlled kinetics
• First passages in bounded domains: When is the mean first passage time meaningful?
• First passages for a search by a swarm of independent random searchers
• Distance matters: the impact of gene proximity in bacterial gene regulation
• First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time
• Diffusive escape through a narrow opening: new insights into a classic problem
• Towards a full quantitative description of single-molecule reaction kinetics in biological cells
• Active colloids in the context of chemical kinetics
• Survival probability of a particle in a sea of mobile traps: A tale of tails
• Uniform asymptotic approximation of diffusion to a small target
• Diffusion in periodic, correlated random forcing landscapes

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